Er-doped superfluorescent fiber source with enhanced mean wavelength stability

ABSTRACT

An erbium-doped (Er-doped) superfluorescent fiber source (SFS) has an enhanced mean wavelength stability. A method determines an estimated mean wavelength of a SFS. The method includes providing an Er-doped SFS having an actual mean wavelength. The method further includes configuring the SFS such that the actual mean wavelength has a dependence on the temperature of the EDF. The method further includes obtaining the dependence of the actual mean wavelength on the temperature of the EDF. The method further includes measuring the temperature of the EDF. The method further includes calculating the estimated mean wavelength using the measured temperature of the EDF and the dependence of the actual mean wavelength on the temperature of the EDF.

RELATED APPLICATION

The present application claims the benefit of priority under 35 U.S.C. §119(e) from U.S. Provisional Application No. 60/415,693, filed on Oct.2, 2002, which is incorporated in its entirety by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to methods and devices forproviding laser light for optical systems and more particularly relatesto superfluorescent fiber sources for providing laser light withenhanced mean wavelength stability.

2. Description of the Related Art

Er-doped superfluorescent fiber sources (SFSs) have been studiedextensively for their application in fiber optic gyroscopes (FOGs). SFSsexhibit a unique combination of high efficiency, high spatial coherence,broad spectral emission, and excellent long-term stability of the meanwavelength. See, e.g., D. G. Falquier, “Erbium doped superfluorescentfiber sources for the fiber optic gyroscope,” Ph. D. dissertation,December 2000, Applied Physics Department, Stanford University,Stanford, Calif.; D. C. Hall et al., “High-stability Er³⁺-dopedsuperfluorescent fiber sources,” J. Lightwave Tech., Vol. 13, No. 7, pp.1452-1460, July 1995; and P. F. Wysocki et al., “Characteristics oferbium-doped superfluorescent fiber sources for interferometric sensorapplications,” J. Lightwave Tech., Vol. 12, No. 3, pp. 550-567, March1994, each of which is incorporated in its entirety by reference herein.

Long term stability of the mean wavelength of the SFS is desirablebecause the scale factor of a FOG scales with the mean wavelength of thesource. Therefore, accurate knowledge of the scale factor, and thus ofthe mean wavelength, is particularly useful for accurate measurements ofthe absolute rotation rate from the FOG. D. C. Hall et al. (cited above)have reported a mean wavelength stability for an Er-doped SFS of theorder of 8 parts per million (ppm). This mean wavelength stability isadequate for low- to medium-accuracy FOGs. However, high-accuracyinertial navigation FOGs utilize a higher stability of the meanwavelength over many hours.

The prior art does not report an SFS with a sufficient mean wavelengthstability for high accuracy applications. One reason for this is that itis difficult to stabilize the various parameters upon which the meanwavelength of an SFS depends (e.g., the wavelength, power, andpolarization of the pump, the temperature and birefringence of thefiber, and the optical feedback returning from the FOG). Previousefforts have provided detailed studies of the contributions of theseindividual parameters to the mean wavelength and have reported variousmethods of effectively reducing these contributions and/or thevariability of these contributions. Besides the exemplary reports ofsuch previous efforts of D. C. Hall et al. and of P. F. Wysocki et al.,both cited above, other exemplary reports include T. Gaiffe et al.,“Wavelength stabilization of an erbium-doped-fiber source with a fiberBragg grating for high-accuracy FOG,” Proc. SPIE, Vol. 2837, pp.375-380, 1996; H. J. Patrick et al., “Erbium-doped superfluorescentfibre source with long period fibre grating wavelength stabilisation,”Electron. Lett., Vol. 33, No. 24, pp. 2061-2063, 1997; M. J. F.Digonnet, “Broadband fiber sources,” in Rare-Earth-Doped Fiber Lasersand Amplifiers, pp. 313-340, 2001, 2^(nd) Edition, M. J. F. Digonnet,Ed., Marcel Dekker, Inc., New York; P. Wysocki et al., “WavelengthStability of a High-Output, Broadband, Er-Doped Superfluorescent FiberSource Pumped near 980 nm,” Opt. Lett., Vol. 16, No. 12, pp. 961-963,June 1991; and P. Z. Zatta et al., “Ultra-high-stability two-stagesuperfluorescent fibre sources for fibre optic gyroscopes,” Electron.Lett., Vol. 38, No. 9, pp. 406-408, April 2002, each of which isincorporated in its entirety by reference herein.

The dependence of the mean wavelength on the pump wavelength has beenpreviously reduced by selecting the pump wavelength appropriately and bystabilizing the laser diode temperature and current. The pump powerdependence of the mean wavelength has been previously reduced by properselection of the pump power and fiber length. Stabilizing the laserdiode temperature and stabilizing the current have also been used toreduce the pump power dependence of the mean wavelength. The effects ofoptical feedback on the mean wavelength can be reduced, and evencancelled, by proper design of the SFS configuration and by opticallyisolating the SFS and the gyro coil. These contributions to the meanwavelength have thus been reduced to a few ppm level or less, butfurther stabilization is still desirable.

SUMMARY OF THE INVENTION

In certain embodiments, a method stabilizes the mean wavelength of lightgenerated by a superfluorescent fiber source (SFS). The method comprisesproviding the SFS. The SFS comprises an Er-doped fiber (EDF) having afirst end, a second end, and a length between the first end and thesecond end. The SFS further comprises a coupler optically coupled to thefirst end of the EDF. The SFS further comprises a pump source opticallycoupled to the coupler. The pump source produces pump light. The meanwavelength is influenced by a wavelength of the pump light. Thewavelength of the pump light depends on the temperature of the pumpsource and depends on the power of the pump light. The pump lightpropagates to the EDF via the coupler. The EDF responds to the pumplight by producing forward amplified spontaneous emission (ASE) lightpropagating away from the pump source and backward ASE light propagatingtowards the pump source. The SFS further comprises a mirror opticallycoupled to the coupler. The mirror reflects the backward ASE light asreflected ASE light which propagates to the EDF. The reflected ASE lightis amplified as it travels through the EDF. The forward ASE light andthe amplified reflected ASE light propagate out of the second end of theEDF. The SFS further comprises an optical isolator coupled to the secondend of the EDF. The forward ASE light and the amplified reflected ASElight from the second end of the EDF are transmitted through the opticalisolator as the SFS output light. The method further comprisesoptimizing the length of the EDF. The method further comprises reducingthe influence of the pump light wavelength on the stability of the meanwavelength.

In certain other embodiments, a superfluorescent fiber source (SFS)generates output light having a mean wavelength with a selectedstability. The SFS comprises an Er-doped fiber (EDF) having a first end,a second end, and a length between the first end and the second end. TheSFS further comprises a coupler optically coupled to the first end ofthe EDF. The SFS further comprises a pump source optically coupled tothe coupler. The pump source produces pump light. The mean wavelength ofthe output light is influenced by a wavelength of the pump light. Thewavelength of the pump light depends on the temperature of the pumpsource and depends on the power of the pump light. The pump lightpropagates to the EDF via the coupler. The EDF responds to the pumplight by producing forward amplified spontaneous emission (ASE) lightpropagating away from the pump source and backward ASE light propagatingtowards the pump source. The SFS further comprises a mirror opticallycoupled to the coupler. The mirror reflects the backward ASE light asreflected ASE light which propagates to the EDF. The reflected ASE lightis amplified as it travels through the EDF. The forward ASE light andthe amplified reflected ASE light propagate out of the second end of theEDF. The SFS further comprises an optical isolator coupled to the secondend of the EDF. The forward ASE light and the amplified reflected ASElight from the second end of the EDF are transmitted through the opticalisolator as the output light. The stability of the mean wavelength ofthe output light is selected by optimizing the length of the EDF andreducing the influence of the pump light wavelength on the meanwavelength.

In certain embodiments, a method determines an estimated mean wavelengthof a superfluorescent fiber source (SFS). The method comprises providingan SFS having an actual mean wavelength. The SFS comprises anerbium-doped fiber (EDF) having a temperature and a pump source. Themethod further comprises configuring the SFS such that the actual meanwavelength has a dependence on the temperature of the EDF. The methodfurther comprises obtaining the dependence of the actual mean wavelengthon the temperature of the EDF. The method further comprises measuringthe temperature of the EDF. The method further comprises calculating theestimated mean wavelength using the measured temperature of the EDF andthe dependence of the actual mean wavelength on the temperature of theEDF.

In certain embodiments, a superfluorescent fiber source (SFS) isprovided. The SFS has a mean wavelength which is stable to withinapproximately ±0.5 part per million over a period of time of at leastone hour.

In certain embodiments, a superfluorscent fiber source (SFS) generatesoutput light having a mean wavelength with a selected stability. The SFScomprises an erbium-doped fiber (EDF) having a length disposed between afirst end and a second end, and the EDF has a temperature. The SFSfurther comprises a pump source controlled to produce pump light at asubstantially constant pump wavelength. The mean wavelength of the SFSis influenced by the pump wavelength. The pump wavelength depends on thetemperature of the pump source and depends on the power of the pumplight. The pump light is coupled to the first end of the EDF topropagate toward the second end of the EDF. The EDF is responsive to thepump light to produce forward amplified spontaneous emission (ASE) lightthat propagates toward the second end of the EDF and is output from thesecond end of the EDF. The EDF is further responsive to the pump lightto produce backward ASE light that propagates toward the first end ofthe EDF. The backward ASE light has a first polarization. The SFSfurther comprises a mirror optically coupled to receive the backward ASElight. The mirror reflects the backward ASE light to produce reflectedASE light at a second polarization orthogonal to the first polarization.The reflected ASE light is coupled to the first end of the EDF and isamplified upon propagating through the length of the EDF to the secondend of the EDF where the amplified reflected ASE light is output withthe forward ASE light. The stability of the mean wavelength is selectedby optimizing the length of the EDF and reducing the influence of thepump wavelength on the mean wavelength.

For purposes of summarizing the invention, certain aspects, advantagesand novel features of the invention have been described herein above. Itis to be understood, however, that not necessarily all such advantagesmay be achieved in accordance with any particular embodiment of theinvention. Thus, the invention may be embodied or carried out in amanner that achieves or optimizes one advantage or group of advantagesas taught herein without necessarily achieving other advantages as maybe taught or suggested herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates a superfluorescent fiber source (SFS)adapted to generate output light having a mean wavelength <λ> inaccordance with embodiments described herein.

FIG. 2 is a flow diagram of an embodiment of a method of determining anestimated mean wavelength <λ_(E)> of an SFS.

FIG. 3 is a plot of the measured actual mean wavelength <λ_(A)> and themeasured ambient temperature T as functions of time during a 50-hourrun.

FIG. 4 plots the measured actual mean wavelength <λ_(A)> as a functionof the measured ambient temperature T.

FIG. 5 is a plot of the difference between the estimated mean wavelength<λ_(E)> and the measured actual mean wavelength <λ_(A)> of FIG. 4 as afunction of time.

FIG. 6 is a plot of the difference for a second set of measurementstaken nine days after the measurement represented in FIG. 5, in whichthe actual mean wavelength <λ_(A)> and the ambient temperature T weremeasured over a 48-hour period.

FIG. 7 is a plot of the difference between the estimated mean wavelength<λ_(E)> and the actual mean wavelength <λ_(A)> of FIG. 6 as a functionof time.

FIG. 8 schematically illustrates one configuration for correcting forthe long-term fluctuations in the wavelength measurements of the opticalspectrum analyzer (OSA).

FIG. 9 illustrates the mean wavelengths, recorded simultaneously, of thelaser diode of the reference source (LD1) and a second laser diode(LD2).

FIG. 10 schematically illustrates a possible cause of the 3-hour to4-hour fluctuations of the OSA readings.

FIG. 11 is a plot of the mean wavelengths of the two laser diodes and ofthe difference between the two wavelengths.

FIG. 12 illustrates the two resultant curves for the mean wavelength ofthe SFS and the wavelength of the laser diode (LD).

FIG. 13 is a plot of the mean wavelength of the SFS after subtractingthe LD curve.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 schematically illustrates a superfluorescent fiber source (SFS)10 to generate SFS output light 12 having a mean wavelength <λ> with aselected stability in accordance with embodiments described herein. TheSFS 10 comprises an Er-doped fiber (EDF) 20 having a first end 22, asecond end 24, and a length between the first end 22 and the second end24. In certain embodiments, the EDF 20 also has a temperature, atemperature-dependent birefringence, and a polarization-dependent gain.The SFS 10 further comprises a coupler 30 optically coupled to the firstend 22 of the EDF 20. In certain embodiments, the coupler 30 has atemperature-dependent birefringence and a polarization-dependent loss.The SFS 10 further comprises a pump source 40 optically coupled to thecoupler 30. The pump source 40 produces pump light 42. The meanwavelength <λ> of the SFS 10 is influenced by the wavelength of the pumplight 42. The wavelength of the pump light 42 is dependent on thetemperature of the pump source 40 and dependent on the power of the pumplight 42. The pump light 42 propagates to the EDF 20 via the coupler 30.The EDF 20 responds to the pump light 42 by producing forward amplifiedspontaneous emission (ASE) light 44 propagating away from the pumpsource 40 and backward ASE light 46 propagating towards the pump source40. The SFS 10 further comprises a mirror 50 optically coupled to thecoupler 30. The mirror 50 reflects the backward ASE light 46 asreflected ASE light 48, which propagates to the EDF 20. The reflectedASE light 48 is further amplified as it travels through the EDF 20. Theforward ASE light 46 and the amplified reflected ASE light propagate outof the second end 24 of the EDF 20. The SFS 10 further comprises anoptical isolator 60 coupled to the second end 24 of the EDF 20. Theforward ASE light 46 and the amplified reflected ASE light from thesecond end 24 of the EDF 20 are transmitted through the optical isolator60 as the SFS output light 12. The stability of the mean wavelength <λ>of the SFS output light 12 is selected by optimizing the length of theEDF 20 and reducing the influence of the pump light 42 wavelength on themean wavelength.

In certain embodiments, the SFS 10 emits light having a wavelength ofapproximately 1550 nanometers and a linewidth of approximately 17nanometers at a power of approximately 5 milliwatts. The linewidth isdefined as described by D. C. Hall et al. in the reference cited above.Other values of the SFS bandwidth, in the range of approximately 1nanometer to approximately 50 nanometers, can be achieved with thisconfiguration and other source configurations by proper selection of thesource parameters, in particular the pump power and the EDF length. Incertain embodiments, the SFS 10 has a double-pass configuration, asillustrated in FIG. 1, which has a greater output power than asingle-pass SFS configuration. Such double-pass configurations can alsouse shorter lengths of the EDF 20 than single-pass configurations andcan enable a Faraday rotation mirror (FRM) to be used to eliminatepolarization-related effects, as described more fully below. Such FRMsare preferable over long Lyot fiber depolarizers which can be used toeliminate polarization-related effects in single-pass configurations ofthe SFS 10.

In certain embodiments, the EDF 20 has a length of at leastapproximately 94 meters, but other lengths are compatible withembodiments described herein. This length is dictated in part by thesource parameters, and in part by the concentration of the trivalenterbium ions in the EDF core. In these particular embodiments, thetrivalent erbium ion concentration in the EDF core is such that thefiber has a small-signal absorption of approximately 3.7 decibels/meterat a wavelength of approximately 1.53 microns. The total small-signalabsorption of the 94-meter fiber at approximately 1.53 microns istherefore approximately 348 decibels. In one advantageous embodiment,the EDF 20 has a core radius of approximately 1.1 microns and anumerical aperture of approximately 0.26. These core parameter values,combined with the total small-signal absorption value of 348 decibels,define a particular set of EDF parameters that optimize the SFS meanwavelength stability, as described more fully below. It should beunderstood, however, that this set is not unique, and that other sets ofparameter values will provide substantially identical behavior. Suchsets can be derived through numerical simulations of the SFS meanwavelength stability using one of several commercially available EDFsimulators. As described more fully below, the length of the EDF 20 canbe selected to reduce the power of the forward ASE light 44, thusreducing drifts of the mean wavelength due to residualpolarization-dependent gain (PDG) effects from the forward ASE light 44.

In certain embodiments, the coupler 30 comprises a wavelength divisionmultiplexer (WDM). Such a WDM coupler 30 transmits substantially all thelight from the pump source 40 at a first wavelength (e.g., 1472nanometers) to the EDF 20. Such a WDM coupler 30 also couplessubstantially all the backward ASE light 46 at a second wavelength(e.g., 1550 nanometers) from the EDF 20 to the mirror 50. Such a WDMcoupler 30 also couples substantially all the reflected ASE light 48 atthe second wavelength from the mirror 50 to the EDF 20. One skilled inthe art will appreciate that an alternative WDM can be used that couplesthe pump light and that transmits the ASE light. When such analternative is used, the positions of the pump source 40 and the mirror50 are interchanged in the embodiment of FIG. 1.

In certain embodiments, the pump source 40 comprises a laser diodehaving a temperature and having a laser diode current (e.g., 10microamps). The pump light 42 of certain embodiments is polarized andcomprises laser light having an infrared wavelength, e.g., betweenapproximately 1460 nanometers and approximately 1490 nanometers.Exemplary laser diodes include, but are not limited to, a 1472-nanometerlaser diode with 30 milliwatts of fiber-pigtailed power. As describedmore fully below, in certain embodiments, the temperature of the pumpsource 40 is controllable to be stable within approximately 0.01 degreeCelsius.

In certain embodiments, the mirror 50 comprises a Faraday rotationmirror (FRM). The mirror 50 of certain embodiments is fiber-pigtailed.FRMs are available commercially from several vendors, e.g., JDS UniphaseCorp. of San Jose, Calif., although many manufacturers offer suchdevices. In certain embodiments, the optical isolator 60 preventstime-dependent reflections at the output of the SFS 10 from introducingundesirable fluctuations in the SFS mean wavelength <λ>. The isolatorisolation ratio is approximately 40 decibels or greater. Higher or lowervalues may be tolerable depending on details of the source design.

Pump Effects

Variations of the temperature of the pump source 40 (e.g., laser diode)can cause corresponding variations in the pump light 42 wavelength λ_(p)generated by the pump source 40. These temperature-induced variations ofthe pump light 42 wavelength can cause corresponding variations in theSFS mean wavelength <λ>.

In certain embodiments, the influence of the pump light variations onthe stability of the mean wavelength are preferably reduced. In certainsuch embodiments, the temperature of the pump source 40 is controlled toa sufficient stability so as to provide a predetermined stability of theSFS mean wavelength <λ>. In certain embodiments, the pump source 40temperature can be controlled to ±0.01 degree Celsius. For a measuredtemperature dependence of a laser diode wavelength of approximately 1nanometer/degree Celsius, the pump light 42 wavelength can thus havevariations Δλ_(p) of approximately ±0.01 nanometer. The magnitude of thecorresponding variations of the SFS mean wavelength <λ> depend on thedependence of the SFS mean wavelength <λ> on the pump light 42wavelength. As used herein, unless otherwise specified, all cited noiseand fluctuation values are peak-to-peak values.

In certain embodiments, the influence of pump light variations on thestability of the SFS mean wavelength <λ> can be reduced by tuning thepump light 42 wavelength λ_(p) to an optimum wavelength (e.g., 1472nanometers) at which the first-order dependence of the SFS meanwavelength <λ> on the pump light 42 wavelength is small or substantiallyzero. In embodiments in which the pump light 42 wavelength differsslightly from the optimum wavelength, a residual dependence of the SFSmean wavelength <λ> on temperature-induced variations of the pump light42 wavelength can be expected. These temperature-induced variations havepreviously been evaluated by modeling the SFS 10 by assuming that thepump light 42 wavelength departs from the optimum wavelength by 1nanometer (see, e.g., M. J. F. Digonnet, “Broadband fiber sources,” inRare-Earth-Doped Fiber Lasers and Amplifiers, pp. 99-101, 2001, 2^(nd)Edition, M. J. F. Digonnet, Ed., Marcel Dekker, Inc., New York, which isincorporated in its entirety by reference herein). The dependence of theSFS mean wavelength <λ> on the pump light 42 wavelength λ_(p) was thencalculated to be δ<λ>/δλ_(p)≈0.015. The variations of the SFS meanwavelength <λ> due to temperature fluctuations of the pump source 40were thus predicted to be only Δ<λ>≈0.00015 nanometer (±0.1 ppm). Thesevariations in the SFS mean wavelength <λ> due to thermally-inducedfluctuations of the pump light 42 wavelength are thus negligible inembodiments in which the pump light 42 wavelength is tuned to or near anoptimum wavelength.

In certain embodiments, the SFS mean wavelength <λ> is dependent on thepump light 42 power, and the pump light 42 power is set to an optimumlevel at which the dependence is small or zero. For example, in certainembodiments, the pump source 40 comprises a laser diode with a currentwhich is maintained at 10 microamps with a pump power stability of 1.3microwatts. The calculated dependence of the SFS mean <λ> on the pumplight 42 power for this pump source 40 was modeled to be −0.085nanometer/milliwatt. Correspondingly, variations of the pump light 42power at the output of the pump source 40 can have a negligible effecton the SFS mean wavelength <λ> (e.g., approximately 0.07 ppm).

While the power from the pump source 40 in certain embodiments isextremely stable, the pump light 42 power launched into the EDF 20 canvary over time. These variations can be due to the combined effects of(1) residual polarization-dependent loss (PDL) in the coupler 30 with(2) random variations in the pump light 42 polarization incident on thecoupler 30 caused by thermal variations in the birefringence of thefiber pigtail between the pump source 40 and the EDF 20. For example, ifthe PDL of the coupler 30 is low (e.g., approximately 0.01 decibel), alaunched power P_(p) of 25 milliwatts will change by approximately 0.05milliwatts as the pump polarization rotates by 90 degrees. Forembodiments in which the dependence of the SFS mean wavelength <λ> onthe launched pump light 42 power |∂<λ>/∂P_(p)| is 0.085nanometer/milliwatt, this variation in the pump light 42 power launchedinto the EDF 20 corresponds to a variation of the SFS mean wavelength<λ> of approximately 3 ppm. Such variations can be undesirably high.However, one should keep in mind that such large variations in thepolarization of the pump incident on the EDF 20 are highly unlikely. Thecalculated 3-ppm variation is a limit unlikely to be reached. Thiseffect can be reduced by selecting a WDM coupler 30 with minimal PDL. Incertain embodiments, selecting such a WDM coupler 30 comprises obtainingand testing WDM couplers from various vendors to isolate those couplerswith sufficiently low PDL. In certain other embodiments, the fiberpigtail between the pump source 40 and the EDF 20 is shortened to reducethis effect. To minimize the polarization excursion, the fiber pigtailtemperature can also be maintained as constant as possible.

In other embodiments, the coefficient |∂<λ>/∂P_(p)| is reduced by properselection of the length of the EDF 20 and proper selection of the pumplight 42 power. However, the EDF 20 length that minimizes |∂<λ>/∂P_(p)|may or may not be sufficient to reduce the single-pass forward ASE light44, as described below in relation to polarization-related effects.Modeling can be used to select a length of the EDF 20 that strikes asuitable compromise between reduction of the dependence of the SFS meanwavelength <λ> on the pump light 42 power and reduction of thesingle-pass forward ASE light 44 contribution. In certain embodiments,the length of the EDF 20 is selected to greatly reduce the single-passforward ASE light 44 contribution without concern of the effect of thislonger length on |∂<λ>/∂P_(p)|. In certain such embodiments,|∂<λ>/∂P_(p)| is low enough so that the overall stability of the SFSmean wavelength <λ> is greatly improved.

Polarization-Related Effects

Polarization-related effects on the SFS mean wavelength <λ> can arisefrom various contributions. In certain embodiments, the polarized natureof the pump light 42 can induce polarization-dependent gain (PDG)effects in the EDF 20. In embodiments in which the SFS 10 has adouble-pass configuration and a standard reflector is used as the mirror50 (rather than an FRM), PDG from the pump light 42 polarization resultsin the two eigenpolarizations of the output light 12 from the SFS 10having substantially different mean wavelengths. The difference of meanwavelengths of the two polarizations can be in excess of 50 ppm. Certainembodiments utilize a polarizer at the input of the FOG to maintainreciprocity. Such effects are described more fully by D. G. Falquier etal., “A depolarized Er-doped superfluorescent fiber source with improvedlong-term polarization stability,” IEEE Photon. Tech. Lett., Vol. 13,pp. 25-27, January 2001; and D. G. Falquier et al., “Apolarization-stable Er-doped superfluorescent fiber source including aFaraday rotator mirror,” IEEE Photon. Tech. Lett., Vol. 12, pp.1465-1467, November 2000. Each of these references is incorporated inits entirety by reference herein. Further information is provided by M.J. F. Digonnet, “Broadband fiber sources,” in Rare-Earth-Doped FiberLasers and Amplifiers, pp. 99-101, 2001, cited above.

Thermal variations in the birefringence of either the EDF 20 or thecoupler 30 can cause fluctuations in the SFS mean wavelength <λ>transmitted to the FOG. Similarly, stress variations of any portion ofthe SFS 10 can modify the birefringence, thereby causing variations ofthe pump light 42 polarization in the EDF 20 and of the SFS meanwavelength <λ>.

Polarization-related drift can be greatly reduced with either Lyotdepolarizers or an FRM. For example, in certain embodiments, using anFRM as the mirror 50 ensures that the polarization of the reflected ASElight 48 is orthogonal to that of the backward ASE light 46 at allpoints along the EDF 20, thereby canceling the effects of PDG. Thus, theuse of an FRM as the mirror 50 can reduce the polarization-dependentvariability of the SFS mean wavelength <λ> (e.g., to approximately 20ppm). In other embodiments, an FRM is used as the mirror 50 inconjunction with other improvements, which further reduces thevariability of the SFS mean wavelength <λ>. This configuration isfurther described by D. G. Falquier et al. in the November 2000reference cited above, and in U.S. Pat. No. 6,483,628 B1 to Digonnet etal., which is incorporated in its entirety by reference herein.

In such embodiments utilizing the FRM as the mirror 50, the single-passforward ASE light 44 is not reflected by the FRM, so the forward ASElight 44 does not experience polarization averaging, and its meanwavelength is still sensitive to polarization. This contribution to thevariability of the SFS mean wavelength <λ> is relatively small since theforward ASE light 44 passes through the EDF 20 only once, and thus hasconsiderably less power than does the double-pass backward ASE light 46.However, this contribution to the variability of the SFS mean wavelength<λ> is partly responsible for the approximately 20-ppm residual meanwavelength variations described by the November 2000 study of D. G.Falquier et al. (cited above), in which perturbations were purposelyapplied to the birefringence of the EDF 20. The length of the EDF 20 canbe selected to reduce the power in the forward ASE light 44, thusreducing variations of the SFS mean wavelength <λ> due to residual PDGeffects from the forward ASE light 44.

In certain embodiments, a polarization controller (PC) is placed betweenthe pump source 40 and the EDF 20 at point A on FIG. 1. The PC isadapted to vary the state of polarization (SOP) of the pump light 42propagating into the EDF 20. Further information on such PCs is providedby U.S. Pat. No. 5,701,318 to Digonnet et al., which is incorporated inits entirety by reference herein. However, in certain such embodiments,the PC exhibits a polarization dependent loss (PDL). The PDL is of theorder of 0.1 decibel at 1570 nanometers and has a smaller value at 1550nanometers. Consequently, adjusting the PC changes the pump light 42power launched into the EDF 20, and thus varies the SFS mean wavelength<λ>. For a PDL at 1480 nanometers of even only 0.02 decibel, thevariations of the SFS mean wavelength <λ> introduced by the PC can beapproximately 8 ppm, or even higher (e.g., 10 to 22 ppm).

In other embodiments, a second PC is placed at the output of the SFS 10at point B in FIG. 1 to measure the dependence of the SFS meanwavelength <λ> on polarization. Residual PDL in the second PC can causean erroneously high reading of the instability of the SFS meanwavelength <λ>. To avoid the corresponding PDL effects on the SFS meanwavelength <λ>, certain embodiments avoid using any PCs which wouldotherwise increase the polarization dependence of the SFS meanwavelength <λ>. In certain such embodiments, as the temperatures ofcomponents of the SFS 10 vary over time, the pump light 42 polarizationalso varies due to temperature-dependent birefringence, but polarizationeffects are not measured directly.

EDF Temperature-Related Effects

Besides the thermal variations of the birefringence of the EDF 20 or thecoupler 30, additional instabilities of the SFS mean wavelength <λ> canbe due to temperature variations of the EDF 20. Variations of thetemperature of the EDF 20 can affect the emission and absorptioncross-sections of erbium. See, e.g., J. Kemtchou et al., “Absorption andemission cross-sections measurements for temperature dependent modelingof erbium-doped fibers amplifiers,” in Proceedings of Third OpticalFibre Measurement Conference, Liege, Belgium, Vol. 1, pp. 93-96, 1995,which is incorporated in its entirety by reference herein. Thesecross-section variations can induce a drift in the mean wavelength ofthe EDF 20 and a corresponding variation in the SFS mean wavelength <λ>.See, e.g., M. J. F. Digonnet, “Broadband fiber sources,” inRare-Earth-Doped Fiber Lasers and Amplifiers, pp. 80-94, 2001, 2^(nd)Edition, M. J. F. Digonnet, Ed., Marcel Dekker, Inc., New York, which isincorporated in its entirety by reference herein.

The thermal coefficient of the temperature dependence of the SFS meanwavelength <λ> depends on characteristics of the EDF 20, as well as theconfiguration and operating parameters of the SFS 10 (e.g., pump light42 wavelength and power). Values of the SFS thermal coefficient rangingfrom −3 to +10 ppm/degree Celsius have previously been measured. See,e.g., D. C. Hall et al., P. Wysocki et al., both cited above, and P. R.Morkel, “Erbium-doped fibre superfluorescent for the fibre gyroscope,”in Optical Fiber Sensors, Springer Proc. in Physics, Vol. 44, pp.143-148, 1989, which is incorporated in its entirety by referenceherein. In certain embodiments, optical filters can be used to furtherreduce the thermal coefficient of the temperature dependence of the SFSmean wavelength <λ>. While the temperature dependence of the SFS meanwavelength <λ> of certain embodiments can be relatively weak, even atemperature dependence of 1 ppm/degree Celsius can lead to unacceptablylarge variations of the SFS mean wavelength <λ> in embodiments in whichthe SFS 10 is required to operate over a wide temperature ranges (e.g.,tens of degrees Celsius).

In certain embodiments, the EDF-temperature effects (including theemission and absorption cross-sections of erbium and thetemperature-dependent polarization-related effects of the EDFbirefringence described above) are reduced by stabilizing the EDFtemperature. However, such embodiments typically utilize higher powerconsumption, longer power-up times, larger sizes, and higher pump source40 costs to keep the SFS mean wavelength <λ> at a predetermined valuewith sufficient stability.

In other embodiments, rather than attempting to keep the SFS meanwavelength <λ> at a predetermined value, it is sufficient to know thevalue of the SFS mean wavelength <λ> at various points in time. The SFSmean wavelength in certain embodiments can be estimated using a measuredtemperature of the EDF 20.

FIG. 2 is a flow diagram of an embodiment of a method 100 of determiningan estimated mean wavelength <λ_(E)> of an SFS 10 (e.g., estimatingvariations of the mean wavelength due to variations of the temperatureof the EDF 20). The method 100 comprises an operational block 110 inwhich an SFS 10 is provided. The SFS 10 has an actual mean wavelength<λ_(A)> and comprises an EDF 20 having a temperature and a pump source40. The method 100 further comprises an operational block 120 in whichthe SFS 10 is configured such that the actual mean wavelength <λ_(A)>has a dependence on the temperature of the EDF 20. The method 100further comprises an operational block 130 in which the dependence ofthe actual mean wavelength <λ_(A)> on the temperature of the EDF 20 isobtained. In certain embodiments, obtaining the dependence of the actualmean wavelength on the temperature of the EDF 20 comprises measuring thetemperature dependence. In other embodiments, obtaining the dependenceof the actual mean wavelength on the temperature of the EDF 20 comprisesobtaining the temperature dependence from another source (e.g.,accessing the results of a previous measurement of the temperaturedependence). The method 100 further comprises an operational block 140in which the temperature of the EDF 20 is measured. The method 100further comprises the operational block 150 in which the estimated meanwavelength <λ_(E)> is calculated using the measured temperature of theEDF 20 and the dependence of the actual mean wavelength <λ_(A)> on thetemperature of the EDF 20.

In certain embodiments, the method 100 does not comprise controlling thetemperature of the EDF 20, while in other embodiments, the method 100comprises controlling the temperature of the EDF 20 to have apredetermined stability (e.g., to be stable within ±0.5 degree Celsius).While certain embodiments of the method 100 do not prevent the actualmean wavelength <λ_(A)> from drifting with temperature, such embodimentsenable the estimated mean wavelength <λ_(E)> to be calculated at anytime. The SFS 10 is preferably configured so that variations of theactual mean wavelength <λ_(A)> are primarily due to variations in thetemperature of the EDF 20. If the actual mean wavelength <λ_(A)> hasappreciable contributions from other temperature-dependent effects(e.g., polarization-related effects such as fiber birefringence),variations in the temperature or in the temperature gradients can alsoaffect other components of the SFS 10. In such embodiments, thecorrelation of the actual mean wavelength <λ_(A)> to the temperature ofthe EDF 20 is reduced, such that the estimated mean wavelength <λ_(E)>is a poorer approximation to the actual mean wavelength <λ_(A)>. See,e.g., M. J. F. Digonnet, “Broadband fiber sources,” in Rare-Earth-DopedFiber Lasers and Amplifiers, pp. 80-94, 2001, cited above.

First Exemplary Embodiment

The following exemplary embodiment illustrates the correlation of theestimated mean wavelength <λ_(E)> with the actual mean wavelength<λ_(A)> for an embodiment in which no attempts were made to control theambient temperature or the temperature of the SFS 10. The SFS 10 wasplaced on an optical table, and an optical spectrum analyzer (OSA) wasused to record the output spectrum of the SFS 10 (and hence the actualmean wavelength <λ_(A)>) every 19 seconds for 50 hours. The OSA used wasModel No. A6327B, manufactured by Ando Electric Co., Ltd. of Kawasaki,Kanagawa, Japan. The ambient temperature was measured and the estimatedmean wavelength <λ_(E)> was calculated.

FIG. 3 is a plot of the measured actual mean wavelength <λ_(A)> and themeasured ambient temperature T as functions of time during the 50-hourrun. In certain embodiments, the temperature T_(EDF) of the EDF 20 isassumed to be approximately equal to the measured ambient temperature T.The measured ambient temperature T, and hence the measured temperatureT_(EDF) of the EDF 20, varied over a range of approximately 2.6 degreesCelsius during the 50 hours of the run. As expected, the measured actualmean wavelength <λ_(A)> also varied substantially (e.g., ±8 ppm).

The actual mean wavelength <λ_(A)> and the measured ambient temperatureT are obviously strongly correlated with one another in FIG. 3. FIG. 4plots the measured actual mean wavelength <λ_(A)> as a function of themeasured ambient temperature T. The measured actual mean wavelength<λ_(A)> is shown to vary almost linearly with the measured temperatureT. Such behavior is expected for small perturbations, as described morefully by D. G. Falquier et al., November 2000, cited above. The smallamount of hysteresis illustrated by FIG. 4 is likely due to a slight lagbetween the measured ambient temperature T and the actual temperatureT_(EDF) of the EDF 20.

A linear fit of the measured actual mean wavelength <λ_(A)> as afunction of the measured ambient temperature T is illustrated in FIG. 4by a straight solid line. Assuming the temperature T_(EDF) of the EDF 20is approximately equivalent to the measured ambient temperature T, thedependence of the actual mean wavelength <λ_(A)> on the temperatureT_(EDF) of the EDF 20 is thus characterized by the equation of thisline, e.g., by the following equation:<λ_(A)>=1564.28055−0.0099149T _(EDF),  (1)where the actual mean wavelength <λ_(A)> has units of nanometers and thetemperature T_(EDF) of the EDF 20 has units of degrees Celsius. Thethermal coefficient of the temperature-dependent SFS mean wavelength <λ>is thus −0.0099 nanometer/degree Celsius, or −6.3 ppm/degree Celsius.Such magnitudes of the temperature dependence of the SFS mean wavelengthare consistent with earlier reported values. See, e.g., D. C. Hall etal. (cited above). Also, see, P. F. Wysocki et al., “Broadband FiberSources for Gyros,” in SPIE Proceedings on Fiber Optic Gyros: 15thAnniversary, Vol. 1585 (SPEE, Washington, 1991), pp. 371-382, which isincorporated in its entirety by reference herein.

In this exemplary embodiment, the measured temperature T_(EDF) of theEDF 20 and the dependence of the actual mean wavelength <λ_(A)> on thetemperature T_(EDF) of the EDF 20 were used to calculate an estimatedmean wavelength <λ_(E)>. Substituting the temperature T_(EDF) of the EDF20 into Equation 1 yielded an estimated mean wavelength <λ_(E)>illustrated by the dotted curve of FIG. 3. FIG. 5 illustrates thedifference between the estimated mean wavelength <λ_(E)> and themeasured actual mean wavelength <λ_(A)>. As shown by FIG. 5, thedifference between the estimated and actual mean wavelengths is withinapproximately ±1 ppm for the full 50 hours of the run.

In this exemplary embodiment, the same measurements were repeated ninedays later, in which the actual mean wavelength <λ_(A)> and the ambienttemperature T were measured over a 48-hour period. FIG. 6 illustratesthese measured values versus time. A linear regression of the measuredactual mean wavelength <λ_(A)> versus the temperature T_(EDF) of the EDF20 (taken to be approximately equivalent to the measured ambienttemperature T) resulted in the following equation:<λ_(A)>=1564.29458−0.010503T _(EDF).  (2)

Again, the measured actual mean wavelength <λ_(A)> and the measuredtemperature T are strongly correlated (see FIG. 6). Using the measuredtemperature T_(EDF) of the EDF 20 and the dependence of the actual meanwavelength <λ_(A)> on the temperature T_(EDF) of the EDF 20 as expressedby Equation 2, an estimated mean wavelength <λ_(E)> was calculated. Thecurve labeled “Estimated mean wavelength using Eq. 2” of FIG. 6illustrates this estimated mean wavelength <λ_(E)>, which agrees verywell with the measured actual mean wavelength <λ_(A)>. The line labeled“Calculated with Eq. 2” of FIG. 7 illustrates the difference betweenthis estimated mean wavelength <λ_(E)> and the actual mean wavelength<λ_(A)> as a function of time. This difference remained withinapproximately ±1 ppm for the full 48 hours of the run.

In embodiments in which the SFS 10 is used as the source for a FOG, theactual mean wavelength of the SFS 10, and hence the gyro scale factor,can be evaluated using the algorithm of FIG. 2 while the FOG is running.Such embodiments measure the temperature of the EDF 20 and determine anestimated mean wavelength while the FOG is running, as described above.However, the temperature dependence of the mean wavelength wouldtypically not be measured in real time, but would be measuredbeforehand. To evaluate how well such embodiments would work, theestimated mean wavelength <λ_(E)> was calculated for the second run, notby using the temperature dependence of Equation 2 (which was measuredduring the second run), but by using the temperature dependence ofEquation 1 (which was measured nine days previously). The resultantestimated mean wavelength <λ_(E)> is illustrated in FIG. 6 as the curvelabeled “Estimated mean wavelength using Eq. 1.” This curve has nearlythe same form as the form of the curve estimated using Equation 2, butthe curve for the “Estimated mean wavelength using Eq. 1” is shiftedtowards shorter wavelengths. This shift has a mean value of 0.0013nanometer, corresponding to approximately 1 ppm. Due to this shift, theresultant difference of the estimated and actual mean wavelengths,illustrated in FIG. 7 by the curve labeled “Calculated with Eq. 1,” isslightly worse than the resultant difference calculated using Equation2, but it still remains within approximately ±2 ppm over the full 48hours of the run.

The offset between the two curves of FIG. 7 originates from the slightdifference between the temperature dependence of the first run(Equation 1) and the temperature dependence of the second run measurednine days later (Equation 2). The SFS 10 was left untouched between thetwo runs, so the offset was likely primarily the result of a drift inthe absolute wavelength reading of the OSA, the temperature of which wasnot controlled.

Using the OSA to measure the spectrum of the broadband source, ashort-term noise of approximately 0.5 to 1 ppm was measured. With ahighly stable 1.55-micron laser diode as a source, and after a warm-uptime of approximately 2 hours, the OSA long-term reading remained withinapproximately ±5 ppm for room temperature variations under approximately±3 degrees Celsius. As explained more fully below, this variation of theOSA long-term reading is expected to be slightly lower for a broadbandlight source, e.g., approximately ±1 ppm/degree Celsius. The differencebetween the temperature dependencies of Equation 1 and Equation 2 couldtherefore easily have been caused by variable temperature gradientsbetween the OSA and the surrounding room. Residual fluctuations in thedifference between the estimated and actual mean wavelengths as shown inFIGS. 5 and 7 were at least partly due to instabilities in the OSA, aswell as due to nonlinearities in the temperature dependence.

As illustrated by this exemplary embodiment, the method 100 of FIG. 2 issuccessful in estimating the mean wavelength within an approximate ±2ppm accuracy over a 48-hour period. In addition, the accuracy can beimproved by improving the stability of the OSA used to measure theactual mean wavelength <λ_(A)>. Furthermore, this exemplary embodimentillustrates that by measuring the ambient temperature over time (whichis assumed to be close to the temperature of the EDF 20), and correctingthe measured mean wavelength for known thermal drift, the meanwavelength of the SFS 10 can be estimated to within approximately ±1 ppmover a time period of 98 hours. This stability represents an importantstep towards a practical high-grade FOG.

Second Exemplary Embodiment

The first exemplary embodiment described above illustrates that aftercorrection of temperature variations of the EDF 20, the SFS meanwavelength <λ> is stable to within approximately ±2 ppm. The firstexemplary embodiment does not provide information regarding thestability of the SFS mean wavelength <λ> if the temperature of the SFS10 were controlled to be stable. In embodiments in which the temperatureof the SFS 10 is controlled to be stable, the stability of the SFS meanwavelength <λ> would likely be better than approximately ±2 ppm, sincestabilizing the temperature of the SFS 10 would not only eliminate thethermal drift of the EDF 20, but other thermal effects as well (e.g.,fiber birefringence drifts and the corresponding residualpolarization-related effects).

The following exemplary embodiment illustrates the correlation of theestimated mean wavelength <λ_(E)> with the actual mean wavelength<λ_(A)> for an embodiment in which the temperature of the SFS 10 waskept relatively stable. The SFS 10 in the following embodiment wassubstantially identical to the SFS 10 described above for the firstexemplary embodiment, except that an EDF 20 having a lower thermalcoefficient was used. All parameters of the pump source 40 werecontrolled to the same tolerance as described above for the firstexemplary embodiment. The small-signal absorption of the EDF 20 at 1.53microns was comparable to that of the EDF 20 (i.e., approximately 348decibels) of the first exemplary embodiment, and forward ASE light 44was also greatly suppressed in this second exemplary embodiment.

To reduce the temperature fluctuations, the EDF 20 and the WDM coupler30 were both placed in a Styrofoam⁷ enclosure. The room temperature wasnot tightly controlled, but the room was kept closed to minimize aircurrents. The room temperature was estimated to be stable to withinapproximately ±0.5 degree Celsius.

As described above with regard to the first exemplary embodiment, thewavelength stability of the pump source 40 exceeds the stability of thestate-of-the-art commercial optical spectrum analyzers (OSAs) used tomeasure the output light from the SFS 10. To correct for the. OSAlong-term fluctuations, the OSA was calibrated using the configuration200 schematically illustrated by FIG. 8. The output light from the SFS10 being tested and the signal from a stable wavelength reference source210 were both transmitted through non-polarization-maintaining (non-PM)fiber pigtails 220 and mixed in a fiber coupler 230 (i.e., a LiNbO₃ 1×2coupler). The reference source 210 was a temperature-controlledcommunication-grade distributed feedback (DFB) laser diode (1541.74nanometers) with a stability of approximately 0.001 nanometer(approximately 0.7 ppm). The mixed light from the coupler 230 was thentransmitted through a polarization-maintaining (PM) fiber pigtail 240 tothe OSA 250. The OSA 250 is connected to a signal processor 252 (e.g.,computer) and a display 254.

The display 254 of the OSA 250 shows the reference wavelength of thereference source 210 superimposed onto the output spectrum from the SFS10, thereby providing an absolute calibration of the wavelength scale ofthe OSA 250. For wavelength drifts in the OSA which are substantiallyuniform across the whole spectrum of the SFS 10 (e.g., approximately1520 nanometers to approximately 1580 nanometers), this configurationfor calibration of the wavelength scale of the OSA 250 is independent ofwavelength drifts. The response of the OSA 250 is dependent on thepolarization of the detected light, so it is desirable to ensure thatthe polarization of the light signal detected by the OSA 250 does notvary over time. This result was accomplished by using a coupler 230comprising a lithium niobate (LiNbO₃) Y-junction with apolarization-maintaining (PM) fiber pigtail, which acted as a polarizer.

The effectiveness of this calibration scheme and the validity of theassumption regarding the uniformity of the wavelength drift were checkedby replacing the SFS 10 by a second DFB laser diode of similar stabilityand wavelength as the reference laser diode 210. FIG. 9 illustrates themean wavelengths, recorded simultaneously, of the laser diode of thereference source 210 (LD1) and the second DFB laser diode (LD2). Bothlaser diodes exhibit (1) short-term noise; (2) quasi-periodicoscillations with a period of approximately 3-4 hours and a peak-to-peakamplitude of approximately 0.002 nanometer; and (3) overallquasi-periodic oscillations with a period of approximately 24 hours anda peak-to-peak amplitude of approximately 0.005 nanometer.

Each of these three components of the temporal behavior of thewavelength fluctuations has a comparable magnitude for the two laserdiodes LD1 and LD2. Each component is a manifestation of the OSAfluctuations on a respective time scale. FIG. 10 schematicallyillustrates an explanation of the 3-hour to 4-hour fluctuations of thedrift component of the OSA readings. At a wavelength λ₁, the OSA readingfluctuates quasi-periodically with a period of approximately 3 to 4hours and an amplitude of approximately 0.002 nanometer. At a differentwavelength (λ₂ or λ₃), the fluctuations have a comparable period andamplitude, but have a different phase than the fluctuations at λ₁. Thisbehavior is consistent with the two wavelengths of FIG. 9, which have3-hour to 4-hour fluctuations which are approximately out of phase withone another. This explanation is also consistent with the observationthat the 3-hour to 4-hour fluctuations are not present in OSA readingsof the SFS mean wavelength. The spectrum from the SFS 10 is broad enough(greater than approximately 10 nanometers) that these fluctuations areaveraged out.

The drift component of the OSA readings with a period of approximately24 hours may arise from periodic variations in the OSA temperature. Toinvestigate this possibility, each of the two curves in FIG. 9 wasaveraged out using a ±3.5-hour time window to eliminate the 3-hour to4-hour component of the OSA fluctuations. The resultant smoothed curvesare shown in FIG. 11, in which the curve for laser diode LD2 wastranslated by approximately 17 nanometers to bring it in the vicinity ofthe LD1 curve. It is apparent from FIG. 11 that the 24-hour oscillationsof the two laser diodes are strongly correlated. FIG. 11 also includesthe difference between these two curves, which is shown to be constantwithin approximately ±1 ppm. Therefore, using the calibration process ofFIG. 8 reduces the OSA long-term drift substantially from its originalapproximately ±5-ppm value.

The configuration illustrated by FIG. 8 was used to simultaneouslymeasure the variations of the mean wavelength of the SFS 10 and of thewavelength of the reference laser diode 210 for 17 hours. FIG. 12illustrates the two resultant curves for the mean wavelength of the SFS10 and the wavelength of the laser diode (LD). The LD wavelength curvewas smoothed with a few-hour integration window, as described above. Asexpected, the long-term variations of the two curves are correlated,which indicates that much of the variations in the SFS mean wavelengthare due to drifts of the OSA.

In certain embodiments, it is preferable to remove the contribution ofthe OSA long-term drift from the mean wavelength of the SFS 10. FIG. 13displays the mean wavelength of the SFS 10 after subtracting the LDwavelength curve. The resultant curve shows that the SFS 10 exhibits amean wavelength stability of approximately ±0.5 ppm over a period of 17hours. In certain other embodiments, the SFS 10 exhibits a meanwavelength stability of approximately ±0.5 ppm over a period of onehour.

The short-term noise of the mean wavelength of the SFS 10 illustrated inFIG. 13 is under approximately ±0.35 ppm, which is limited by the OSAperformance. Since the SFS temperature variations during this run wereestimated to be at least approximately ±0.5 degree Celsius, the thermalcoefficient of this SFS 10 was at most approximately 0.7 ppm/degreeCelsius, or about one order of magnitude smaller than the first SFS 10.This value of the thermal coefficient of the SFS 10 falls within therange of previously reported values. See, e.g., D. C. Hall et al., P.Wysocki et al., June 1991, and P. R. Morkel, each of which is citedabove. The thermal coefficient of the SFS 10 has a complex dependence onmany parameters (e.g., the temperature dependence of the erbiumcross-section spectra) which are difficult to measure. It is thereforegenerally difficult to predict the thermal coefficient theoretically, orto justify why one fiber performs better than another.

In the exemplary embodiments described above, the stability of the meanwavelength of the SFS 10 was not tested against all possible states ofpolarization (SOPs) of the pump light 42 or the ASE light 44, 46. Suchtests would typically utilize polarization controllers, which introducePDL effects on the mean wavelength, and artificially increase theinstability of the mean wavelength of the SFS 10. Nevertheless, thefirst and second exemplary embodiments illustrate unambiguously thatwith SFS temperature excursions of approximately ±0.5 degree Celsius,the birefringence in the SFS 10 is stable enough to attain a meanwavelength stability of approximately ±0.5 ppm. When temperaturefluctuations are larger, the mean wavelength of the SFS 10 can becalculated to within approximately ±2 ppm of its actual value bymeasuring the temperature of the SFS 10. The resultant stability of themean wavelength is probably limited by the stability of the instrumentused to measure the mean wavelength. It is thus possible to stabilize anEr-doped SFS 10 to meet the accuracy requirements of inertial navigationFOGs.

Various embodiments of the present invention have been described above.Although this invention has been described with reference to thesespecific embodiments, the descriptions are intended to be illustrativeof the invention and are not intended to be limiting. Variousmodifications and applications may occur to those skilled in the artwithout departing from the true spirit and scope of the invention asdefined in the appended claims.

1. A method of stabilizing the mean wavelength of light generated by asuperfluorescent fiber source (SFS), the method comprising: providingthe SFS, the SFS comprising: an Er-doped fiber (EDF) having a first end,a second end, and a length between the first end and the second end; acoupler optically coupled to the first end of the EDF; a pump sourceoptically coupled to the coupler, the pump source producing pump light,the mean wavelength influenced by a wavelength of the pump light, thewavelength of the pump light dependent on the temperature of the pumpsource and dependent on the power of the pump light, the pump lightpropagating to the EDF via the coupler, whereby the EDF responds to thepump light by producing forward amplified spontaneous emission (ASE)light propagating away from the pump source and backward ASE lightpropagating towards the pump source; a mirror optically coupled to thecoupler, whereby the mirror reflects the backward ASE light as reflectedASE light which propagates to the EDF, the reflected ASE light amplifiedupon traveling through the EDF, the forward ASE light and the amplifiedreflected ASE light propagating out of the second end of the EDF; and anoptical isolator coupled to the second end of the EDF, the forward ASElight and the amplified reflected ASE light from the second end of theEDF being transmitted through the optical isolator as the SFS outputlight; optimizing the length of the EDF, wherein the optimizing thelength of the EDF comprises selecting the length to compromise betweenreduction of the dependence of the mean wavelength on the pump lightpower and reduction of the contribution of the forward ASE light to theoutput light; and reducing the influence of the pump light wavelength onthe stability of the mean wavelength.
 2. The method of claim 1, whereinthe method further comprises reducing variations of the temperature ofthe EDF.
 3. The method of claim 1, wherein the method further comprisesestimating variations of the mean wavelength due to variations of thetemperature of the EDF.
 4. The method of claim 1, wherein reducing theinfluence of the pump light wavelength on the stability of the meanwavelength comprises reducing variations of the temperature of the pumpsource.
 5. A method of stabilizing the mean wavelength of lightgenerated by a superfluorescent fiber source (SFS), the methodcomprising: providing the SFS, the SFS comprising: an Er-doped fiber(EDF) having a first end, a second end, and a length between the firstend and the second end; a coupler optically coupled to the first end ofthe EDF; a pump source optically coupled to the coupler, the pump sourceproducing pump light, the mean wavelength influenced by a wavelength ofthe pump light, the wavelength of the pump light dependent on thetemperature of the pump source and dependent on the power of the pumplight, the pump light propagating to the EDF via the coupler, wherebythe EDF responds to the pump light by producing forward amplifiedspontaneous emission (ASE) light propagating away from the pump sourceand backward ASE light propagating towards the pump source; a mirroroptically coupled to the coupler, whereby the mirror reflects thebackward ASE light as reflected ASE light which propagates to the EDF,the reflected ASE light amplified upon traveling through the EDF, theforward ASE light and the amplified reflected ASE light propagating outof the second end of the EDF; and an optical isolator coupled to thesecond end of the EDF, the forward ASE light and the amplified reflectedASE light from the second end of the EDF being transmitted through theoptical isolator as the SFS output light; optimizing the length of theEDF wherein the optimizing the length of the EDF comprises selecting thelength to compromise between reduction of the dependence of the meanwavelength on the pump light power and reduction of the contribution ofthe forward ASE light to the output light; and reducing the influence ofthe pump light wavelength on the stability of the mean wavelength,wherein reducing the influence of the pump light wavelength on thestability of the mean wavelength comprises tuning the pump source to awavelength at which a first-order dependence of the mean wavelength onthe pump light wavelength is small or substantially zero.
 6. Asuperfluorescent fiber source (SFS) to generate output light having amean wavelength with a selected stability, the SFS comprising: anEr-doped fiber (EDF) having a first end, a second end, and a lengthbetween the first end and the second end; a coupler optically coupled tothe first end of the EDF; a pump source optically coupled to thecoupler, the pump source producing pump light, the mean wavelength ofthe output light influenced by a wavelength of the pump light, thewavelength of the pump light dependent on the temperature of the pumpsource and dependent on the power of the pump light, the pump lightpropagating to the EDF via the coupler, whereby the EDF responds to thepump light by producing forward amplified spontaneous emission (ASE)light propagating away from the pump source and backward ASE lightpropagating through the first end of the EDF and through the coupler; amirror optically coupled to the coupler, whereby the mirror reflects thebackward ASE light as reflected ASE light propagating through thecoupler, the reflected ASE light amplified upon traveling through theEDF, the forward ASE light and the amplified reflected ASE lightpropagating out of the second end of the EDF; and an optical isolatorcoupled to the second end of the EDF, the forward ASE light and theamplified reflected ASE light from the second end of the EDF beingtransmitted through the optical isolator as the output light, whereinthe length of the EDF is optimized to compromise between reduction ofdependence of the mean wavelength on the pump light power and reductionof the contribution of the forward ASE light to the output light.
 7. TheSFS of claim 6, wherein the stability of the mean wavelength of theoutput light is further selected by reducing variations of thetemperature of the EDF.
 8. The SFS of claim 6, wherein the stability ofthe mean wavelength of the output light is further selected byestimating variations of the mean wavelength due to variations of thetemperature of the EDF.
 9. The SFS of claim 6, wherein the selectedstability is within approximately ±0.5 part per million over a period oftime of at least one hour.
 10. The SFS of claim 6, wherein the selectedstability is within approximately ±0.5 part per million over a period oftime of at least 17 hours.
 11. The SFS of claim 6, wherein the EDF has asmall-signal absorption of at least approximately 340 decibels.
 12. TheSFS of claim 6, wherein the coupler comprises a wavelength-divisionmultiplexer.
 13. The SFS of claim 12, wherein the wavelength-divisionmultiplexer has a polarization-dependent loss (PDL) less thanapproximately 0.01 decibel.
 14. The SFS of claim 6, wherein the SFS hasno polarization controller.
 15. A superfluorescent fiber source (SFS) togenerate output light having a mean wavelength with a selectedstability, the SFS comprising: an Er-doped fiber (EDF) having a firstend, a second end, and a length between the first end and the secondend; a coupler optically coupled to the first end of the EDF; a pumpsource optically coupled to the coupler, the pump source producing pumplight, the mean wavelength of the output light influenced by awavelength of the pump light, the wavelength of the pump light dependenton the temperature of the pump source and dependent on the power of thepump light, the pump light propagating to the EDF via the coupler,whereby the EDF responds to the pump light by producing forwardamplified spontaneous emission (ASE) light propagating away from thepump source and backward ASE light propagating through the first end ofthe EDF and through the coupler, wherein the pump source comprises alaser diode having a temperature and a laser diode current, whereby thetemperature is controllable to be stable within approximately ±0.01degree Celsius and the laser diode current is controllable to beapproximately 10 microamps; a mirror optically coupled to the coupler,whereby the mirror reflects the backward ASE light as reflected ASElight propagating through the coupler, the reflected ASE light amplifiedupon traveling through the EDF, the forward ASE light and the amplifiedreflected ASE light propagating out of the second end of the EDF; and anoptical isolator coupled to the second end of the EDF, the forward ASElight and the amplified reflected ASE light from the second end of theEDF being transmitted through the optical isolator as the output light,wherein the length of the EDF is optimized to compromise betweenreduction of dependence of the mean wavelength on the pump light powerand reduction of the contribution of the forward ASE light to the outputlight.
 16. A superfluorscent fiber source (SFS) that generates outputlight having a mean wavelength with a selected stability, the SFScomprising: an erbium-doped fiber (EDF) having a length disposed betweena first end and a second end; a pump source controlled to produce pumplight at a substantially constant pump wavelength, the mean wavelengthof the SFS influenced by the pump wavelength, the pump wavelengthdependent on the temperature of the pump source and dependent on thepower of the pump light, the pump light coupled to the first end of theEDF to propagate toward the second end of the EDF, the EDF responsive tothe pump light to produce forward amplified spontaneous emission (ASE)light that propagates toward the second end of the EDF and is outputfrom the second end of the EDF, the EDF further responsive to the pumplight to produce backward ASE light that propagates toward the first endof the EDF, the backward ASE light having a first polarization; and amirror optically coupled to receive the backward ASE light, the mirrorreflecting the backward ASE light to produce reflected ASE light at asecond polarization orthogonal to the first polarization, the reflectedASE light coupled to the first end of the EDF and amplified uponpropagating through the length of the EDF to the second end of the EDFwhere the amplified reflected ASE light is output with the forward ASElight, whereby the stability of the mean wavelength is selected byoptimizing the length of the EDF to compromise between reduction ofdependence of the mean wavelength on the pump light power and reductionof the contribution of the forward ASE light to the output light andreducing the influence of the pump wavelength on the mean wavelength.17. The SFS of claim 16, wherein the stability of the mean wavelength isfurther selected by reducing variations of the temperature of the EDF.18. The SFS of claim 16, wherein the stability of the mean wavelength isfurther selected by accounting for variations of the temperature of theEDF.
 19. The SFS of claim 16, wherein the selected stability is withinapproximately ±0.5 part per million over a period of time of at leastone hour.
 20. The SFS of claim 16, wherein the selected stability iswithin approximately ±0.5 part per million over a period of time of atleast 17 hours.
 21. A superfluorescent fiber source (SFS) to generateoutput light having a mean wavelength with a selected stability, the SFScomprising: an Er-doped fiber (EDF) having a first end, a second end,and a length between the first end and the second end; a coupleroptically coupled to the first end of the EDF; a pump source opticallycoupled to the coupler, the pump source producing pump light, the meanwavelength influenced by a wavelength of the pump light, the wavelengthof the pump light dependent on the temperature of the pump source anddependent on the power of the pump light, the pump light propagating tothe EDF via the coupler, whereby the EDF responds to the pump light byproducing forward amplified spontaneous emission (ASE) light propagatingaway from the pump source and backward ASE light propagating towards thepump source; a mirror optically coupled to the coupler, whereby themirror reflects the backward ASE light as reflected ASE light whichpropagates to the EDF, the reflected ASE light amplified upon travelingthrough the EDF, the forward ASE light and the amplified reflected ASElight propagating out of the second end of the EDF; and an opticalisolator coupled to the second end of the EDF, the forward ASE light andthe amplified reflected ASE light from the second end of the EDF beingtransmitted through the optical isolator as the SFS output light,wherein the mean wavelength of output light has a stability dependent onthe length of the EDF, the pump source having a wavelength at which afirst order dependence of the mean wavelength on the pump lightwavelength is small or substantially zero, wherein the length of the EDFcompromised between reduction of dependence of the mean wavelength onthe pump light power and reduction of the contribution of the forwardASE light to the output light.
 22. A superfluorescent fiber source (SFS)to generate output light having a mean wavelength with a selectedstability, the SFS comprising: an Er-doped fiber (EDF) having a firstend, a second end, and a length between the first end and the secondend; a coupler optically coupled to the first end of the EDF; a pumpsource optically coupled to the coupler, the pump source producing pumplight, the mean wavelength influenced by a wavelength of the pump light,the wavelength of the pump light dependent on the temperature of thepump source and dependent on the power of the pump light, the pump lightpropagating to the EDF via the coupler, whereby the EDF responds to thepump light by producing forward amplified spontaneous emission (ASE)light propagating away from the pump source and backward ASE lightpropagating towards the pump source; a mirror optically coupled to thecoupler, whereby the mirror reflects the backward ASE light as reflectedASE light which propagates to the EDF, the reflected ASE light amplifiedupon traveling through the EDF, the forward ASE light and the amplifiedreflected ASE light propagating out of the second end of the EDF; and anoptical isolator coupled to the second end of the EDF, the forward ASElight and the amplified reflected ASE light from the second end of theEDF being transmitted through the optical isolator as the SFS outputlight, wherein the mean wavelength of output light has a stabilitydependent on the length of the EDF, the length compromising betweenreduction of the dependence of the mean wavelength on the pump lightpower and reduction of the contribution of the forward ASE light tooutput light.